LEAST-SQUARES OPTIMAL LINEARIZATION

Optimal Linearization approximates a nonlinear system function by a best linear model over a specified region of states and controls. It is designed to improve upon conventional linearization and is different from other methods of linearization. This paper presents the theoretical solutions to square norm optimal linearization, derives a numerical algorithm for its implementation, and discusses its use in feedback design. The least squares optimal linearization has a unique solution over a hypercubic region. The optimal linear matrices are proper multiple integrals of the nonlinear function. Conventional linearization is the limiting case of optimal linearization where the region of interest is very small. In particular, the numerical algorithm computes conventional linear matrices efficiently. In general, optimal Linear models are closer to given nonlinear systems than conventional linear models. Three examples are given to demonstrate the concept of optimal linearization. Optimal linearization applies to any continuous nonlinear functions and gives rise to sound numerical methods. Overall, it presents a new framework for linearizing nonlinear systems.